In a pioneering experiment, Hanbury Brown and Twiss (HBT) demonstrated that noise correlations could be used to probe the properties of a (bosonic) particle source through quantum statistics; the effect relies on quantum interference between possible detection paths for two indistinguishable particles. HBT correlations--together with their fermionic counterparts--find numerous applications, ranging from quantum optics to nuclear and elementary particle physics. Spatial HBT interferometry has been suggested as a means to probe hidden order in strongly correlated phases of ultracold atoms. Here we report such a measurement on the Mott insulator phase of a rubidium Bose gas as it is released from an optical lattice trap. We show that strong periodic quantum correlations exist between density fluctuations in the expanding atom cloud. These spatial correlations reflect the underlying ordering in the lattice, and find a natural interpretation in terms of a multiple-wave HBT interference effect. The method should provide a useful tool for identifying complex quantum phases of ultracold bosonic and fermionic atoms.

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We investigate the phase coherence properties of ultracold Bose gases in optical lattices, with special emphasis on the Mott insulating phase. We show that phase coherence on short length scales persists even deep in the insulating phase, preserving a finite visibility of the interference pattern observed after free expansion. This behavior can be attributed to a coherent admixture of particle/hole pairs to the perfect Mott state for small but finite tunneling. In addition, small but reproducible "kinks" are seen in the visibility, in a broad range of atom numbers. We interpret them as signatures for density redistribution in the shell structure of the trapped Mott insulator. [5,6,7,8], or the superfluid to Mott insulator (MI) transition undergone in optical lattices [9,10,11].For a Bose-Einstein condensate released from an optical lattice, the density distribution after expansion shows a sharp interference pattern [10]. In a perfect Mott Insulator, where atomic interactions pin the density to precisely an integer number of atoms per site, phase coherence is completely lost and no interference pattern is expected. The transition between these two limiting cases happens continuously as the lattice depth is increased. In the superfluid phase, a partial loss of long range coherence due to an increased quantum depletion has been observed for lattice depths below the MI transition [12,13,14]. Conversely, in the insulating phase, numerical simulations [15,16,17] predict a residual interference, although long-range coherence and superfluidity have vanished.In this Letter, we revisit this question of phase coherence focusing on the insulating phase. We observe that the interference pattern persists in the MI phase, and that its visibility decays rather slowly with increasing lattice depth. We explain this behavior as a manifestation of short-range coherence in the insulating phase, fundamentally due to a coherent admixture of particle/hole pairs to the ground state for large but finite lattice depths. In addition, we also observe reproducible "kinks" in the visibility at well-defined lattice depths. We interpret them as signature of density redistribution in the shell structure of a MI in an inhomogeneous potential, when regions with larger-than-unity filling form. Finally, the issue of adiabatic loading in the lattice is briefly discussed.In our experiment, a 87 Rb Bose-Einstein condensate is loaded into an optical lattice created by three orthogonal pairs of counter-propagating laser beams (see [10] for more details). The superposition of the lattice beams, derived from a common source at a wavelength λ L = 850 nm, results in a simple cubic periodic potential with a lattice spacing d = λ L /2 = 425 nm. The lattice depth V 0 is controlled by the laser intensities, and is measured here in units of the single-photon recoil energy,where m is the atomic mass. The optical lattice is ramped up in 160 ms, using a smooth waveform that minimizes sudden changes at both ends of the ramp. After switching off the optical and magne...

We demonstrate single-site addressability in a two-dimensional optical lattice with 600 nm lattice spacing. After loading a Bose-Einstein condensate in the lattice potential, we use a focused electron beam to remove atoms from selected sites. The patterned structure is subsequently imaged by means of scanning electron microscopy. This technique allows one to create arbitrary patterns of mesoscopic atomic ensembles. We find that the patterns are remarkably stable against tunneling diffusion. Such microengineered quantum gases are a versatile resource for applications in quantum simulation, quantum optics, and quantum information processing with neutral atoms.

We report on precision measurements of spin-dependent interaction-strengths in the 87 Rb spin-1 and spin-2 hyperfine ground states. Our method is based on the recent observation of coherence in the collisionally driven spin-dynamics of ultracold atom pairs trapped in optical lattices. Analysis of the Rabi-type oscillations between two spin states of an atom pair allows a direct determination of the coupling parameters in the interaction hamiltonian. We deduce differences in scattering lengths from our data that can directly be compared to theoretical predictions in order to test interatomic potentials. Our measurements agree with the predictions within 20%. The knowledge of these coupling parameters allows one to determine the nature of the magnetic ground state. Our data imply a ferromagnetic ground state for 87 Rb in the f = 1 manifold, in agreement with earlier experiments performed without the optical lattice. For 87 Rb in the f = 2 manifold the data points towards an antiferromagnetic ground state, however our error bars do not exclude a possible cyclic phase.